Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory

We propose various ways of adding mass terms to three-dimensional twistor string theory. We begin with a review of mini-twistor space--the reduction of D=4 twistor space to D=3. We adapt the two proposals for twistor string theory, Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model, we identify the enhanced R-symmetry. We then construct B-model topological string theories that, we propose, correspond to D=3 Yang-Mills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits's model. Some of our constructions can be lifted to D=4, where infinitesimal mass terms correspond to VEVs of certain superconformal gravity fields.Comment: 69 pages; Typos correcte

Elasto-multi-body dynamics of internal combustion engines with thin-shell elastohydrodynamic journal bearings

This thesis describes problems associated with noise and vibration concern in internal combustion engines as the result of a growing trend in the development of modern vehicular engines with high power to light weight ratios. There are a plethora of vibration concerns. These are owed to the increasing combustion forces in lean burn engines and the progressive use of materials of durable, but light-weight construction. The latter has come about as a result of a need to reduce the inertial imbalances. These features have resulted in achieving fuel efficiency. Although the primary aims in high output power and structural integrity have been largely achieved, these have culminated in an assortment of sources of noise and vibration, chiefly among them those associated with signature output of the combustion process. For the common four stroke engines, the contributory sources are at half-engine order multiples, referred to as engine "roughness". A holistic approach is to incorporate reduced engine roughness contributions as an integral part of engine design and development. The aim of this thesis is to create a methodology for fundamental design evaluation and analysis of engine dynamics, which comprises rigid body inertial dynamics of engine assembly, the elasto-dynamics of flexible and compliant components and applied and reactive forces in such a complex assembly. [Continues.

Roots of bivariate polynomial systems via determinantal representations

We give two determinantal representations for a bivariate polynomial. They may be used to compute the zeros of a system of two of these polynomials via the eigenvalues of a two-parameter eigenvalue problem. The first determinantal representation is suitable for polynomials with scalar or matrix coefficients, and consists of matrices with asymptotic order $n^2/4$, where $n$ is the degree of the polynomial. The second representation is useful for scalar polynomials and has asymptotic order $n^2/6$. The resulting method to compute the roots of a system of two bivariate polynomials is competitive with some existing methods for polynomials up to degree 10, as well as for polynomials with a small number of terms.Comment: 22 pages, 9 figure